(ii) If \(C_{p}(Y)\)  is a barrelled lcs, i.e. every closed absolutely convex absorbing set in \(C_{p}(Y)\)  is a neighbourhood of zero,
(see [1]}),
then the implication (3) \(\Rightarrow \)  (2) of Theorem REF  holds for each \(C_{p}(X)\) .
